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Seems like you missed the point. I mentioned the example of Joseph Curwen as an illustration, not as evidence. The basic point is that it does not matter how famous/obscure someone is, if they just stay young forever, people will notice. And the idea is that they prefer to remain unnoticed. So the obvious solution is to kill off the old identities every so often and start over in some other place under some new identity.
So that makes it clear that there is no inconsistency in Cochrane's scenario. As long as they are immortal, they will have to keep switching identities or their anonymity is compromised.
Maybe it's just because I'm familiar with his general attitude, but I think it is very clear he is joking. I pointed out in my other comment that he's talked about this before, and he makes it clear that he thinks that longevity research is underfunded because elites are ignorant of the possibilities. He's comically assuming the opposite: that elites ignore longevity research for the only rational reason: because they are already immortal. If it has to be explained it isn't as funny, I suppose.